A Table Theorem for Surfaces with Odd Euler Characteristic

TL;DR

This paper proves a generalized table theorem for functions on Riemannian surfaces with odd Euler characteristic, and applies it to confirm the table conjecture for even functions on the sphere.

Contribution

It introduces a new generalized table theorem for surfaces with odd Euler characteristic and applies it to solve the table conjecture on the sphere.

Findings

Proved a generalized table theorem for surfaces with odd Euler characteristic.

Confirmed the table conjecture for even functions on the two sphere.

Utilized the square peg problem for smooth curves in the proof.

Abstract

We use the square peg problem for smooth curves to prove a generalized table Theorem for real valued functions on Riemannian surfaces with odd Euler characteristic. We then use this result to prove the table conjecture for even functions on the two sphere.